Variance

back to [[Statistical Dispersion]]

The '''variance'''  of a set of data is the mean of the sum of squared deviations from the [[Arithmetic Mean]] of the same set of data. Because this calculation sums the squared deviations, the unit of variance is the square of the unit of observation. Thus, the variance of a set of heights measured in inches will be given in square inches. This fact is inconvenient and has motivated statisticians to call the square root of the variance, the [[Standard Deviation]] and to quote this value as a summary of dispersion.

When the set of data is a [[Population]], we call this the ''population variance''. If the set is a [[Sample]], we call it the ''sample variance''.

The method of calculation is easily understood from the table below where the mean is 8.

    i   x[i]   x[i]-mean   (x[i]-mean)^2
    1     5        -3            9
    2     7        -1            1
    3     8         0            0
    4    10         2            4
    5    10         2            4
   ---  ----       ---          ---
   n=5  sum=40      0           18

   mean = 40/5 = 8
   variance = 18/5 = 3.6
   standard deviation = 1.897366596101


Note that the column of deviations sums to zero. This is always the case. 
----
[[Dick Beldin]]